Improper Integral Convergence

Homework Statement

I'm trying to show that this improper integral converges
$$\int_{0}^{1} \sin \left ( x + \frac{1}{x} \right )dx$$

The Attempt at a Solution

I thought a comparison test would be nice but I can't think of the right one if that is the way to go. I don't think a substitution of u = x + 1/x works too well as well.

Thanks.